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Tagged with notation random-variables
76 questions
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Notation for manipulation of random variables
Let X and Y be two independent random variables. If X and Y are both
standard normal, then what is the distribution of the random variable
$\frac{1}{2}(X^2+Y^2)$?. (Sahoo, Prob and Math Stat, Review 8....
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Is $P((X\in A)\cap(Y\in B))=P((X,Y)\in A\times B)$?
I'm currently working on real valued random variables and I wonder if the following notation exists.
Given $P$ a probability measure on some set $\Omega$, two real valued random variables $X$ and $Y$ ...
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Is $P(A,B) := P(A \cap B)$ per definition? [duplicate]
In the notation for probability and statistics I frequently see a tuple of values fed into a probability measure. For instance, consider $$P(X = x, Y = x)$$
which can be rewritten as $$ P(X^{-1}x, Y^{-...
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Weird syntax in MIT Statistic For Applications course
I'm new to statistics and I'm completely stuck on the first question from an online MIT course.
The full question is here (first question):
https://github.com/hoangnguyen7699/...
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What does $\mathbb{P}[X=a,Y=b]$ mean, notationally?
I am wondering what the notation $\mathbb{P}[X=a,Y=b]$ means- for random variables $X$ and $Y$, where $a$ and $b$ are values they respectively take on- I know that $\mathbb{P}[X=a]$ is the probability ...
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Understanding terminal $\sigma-$algebra and related notation
I need some clarification about this "statement" in my notes, which I find unclear and I could not find anything really comprehensive around. I am studying for an exam so it's important.
&...
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Probabilistic notation for the multivariate normal distributions and joint probability distribution functions
Suppose I have two Random Variables $X$ and $Y$:
X ~ $\mathcal{N}(\mu_1, \sigma_1^2)$
Y ~ $\mathcal{N}(\mu_2, \sigma_2^2)$
Provide that $X$ and $Y$ are independent, I have often seen these two ...
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Random variable notation when writing down probability distributions
I want to discuss discrete random variables that take on outcomes from some finite set. Is there a sense in which every probability distribution is associated with a random variable and vice versa?
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Notation: x randomly chosen with weights from set S
I have implemented $\epsilon$-greedy policy in the context of reinforcement learning in Python code:
...
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Notation for random variable times indicator function
Is the following notation of common use? For a random variable $X$ and an event $A$, $X\mathbb{1}_A$ is denoted as $(X|A)$? I find it in the following paper (the random variable is $\pi_i$ and the ...
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Order Statistics Notation
According to Wikipedia...
For example, suppose that four numbers are observed or recorded resulting in a sample of size $4$. If the sample values are $6, 9, 3, 8$, the order statistics would be ...
- 2,128
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Understanding random variables as functions
First of all, I have read What is a function and I have understood it basically and it is clear to me that in order to caluclate statistics "things" have to be transformed or mapped to ...
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Notation about convergence of random variables
This is a simplification of this question Can two sequences of r.v be asymptotically equivalent? , in order to favour contributions without having a long question.
The central limit theorem is stated ...
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Realization vs Random Variables in Formulae
Currently reading through: https://web.math.princeton.edu/~rvan/APC550.pdf. Page 8 Section 1.2.1 says:
If $X_1$, $X_2, ...$ are i.i.d random variables, then
$$ \frac{1}{n}\sum^n_{k=1} X_k - \mathbf{E}[...
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What am I writing when I write $\mathbf X \mid \mathbf Y$?
Suppose $\mathbf X$ is a random variable and $A$ is an event in the same probability space $(\Omega, \mathcal F, \Pr)$. (Formally, $\mathbf X$ is a function on $\Omega$, say $\Omega \to \mathbb R$; $A$...
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